Model IV Manufacturing model with shortage 1 Demand D is uniform at a rate of runits per unit time 2 Production rate is finite say kor units per unit time 3 Shortages are allowed and have logged 4 Zero lead time 5 C inventory carrying cost per unit time 6 C shortage cost per unit line 7 Cs set up cost per run Optimal order quantity S v Over all annual cent 1000x100 2DC Cs C 1 01 306 Minimum cost Q Q G 1 G C t minimum cost in r Cs Q Solution k 2csr C C C 1 F 2r C C Cs 1 7 C C Worked Example 1 An item is produced at the rate of 50 items per day The demand occuss at the rate of 25 items per day If the setup cost is Rs 100 per set up and holding cost is Rs 0 01 per unit of item per day Find the economics lot size for one run assumes that the shortages are not allowed Also find the time fo cycle and the minimum total cost of one run 100000 2x1000x20x160x Rs 2 csr C C C C 1 1 50 perday 25 per days Rs 100 D 001 63